This invention relates to radio frequency coils for magnetic resonance (MR) applications. In particular, the invention is directed to asymmetric radio frequency coils for magnetic resonance imaging (MRI) machines.
In certain of its aspects, the invention provides methods for designing radio frequency coils for magnetic resonance applications which may be symmetric or asymmetric.
The radio frequency coils of the invention may be used for transmitting a radio frequency field, receiving a magnetic resonance signal, or both transmitting a radio frequency field and receiving a magnetic resonance signal. When the radio frequency coil serves a transmitting function, it will normally be combined with a shield to reduce magnetic interference with external components of the magnetic resonance imaging system.
In magnetic resonance imaging (MRI) applications, a patient is placed in a strong and homogeneous static magnetic field, causing the otherwise randomly oriented magnetic moments of the protons, in water molecules within the body, to precess around the direction of the applied field. The part of the body in the homogeneous region of the magnet is then irradiated with radio-frequency (RF) energy, causing some of the protons to change their spin orientation. The net magnetization of the spin ensemble is nutated away from the direction of the applied static magnetic field by the applied RF energy. The component of this net magnetization orthogonal to the direction of the applied static magnetic field acts to induce measurable signal in a receiver coil tuned to the frequency of precession. This is the magnetic resonance (MR) signal.
The useful RF components are those generated in at plane at 90 degrees to the direction of the static magnetic field. The same coil structure that generates the RF field can be used to receive the MR signal or a separate receiver coil placed close to the patient may be used. In either case the coils are tuned to the Larmor precessional frequency xcfx890 where xcfx890=xcex3B0 and xcex3 is the gyromagnetic ratio for a specific nuclide and B0 is the applied static magnetic field.
A desirable property of radio frequency coils for use in MR is the generation of homogeneous RF fields over a prescribed region. Normally this region is central to the coil structure for transmission resonators. A well known example of transmission resonators is the birdcage resonator, details of which are given by Hayes et. al. in The Journal of Magnetic Resonance, 63, 622 (1985) and U.S. Pat. No. 4,694,255.
In some circumstances it is desirable to generate a target field over an asymmetric region of the coil structure, i.e., a region that is asymmetric relative to the mid-length point of the longitudinal axis of the coil structure. This is potentially advantageous for patient access, conformation of the coil structure to the local anatomy of the patient and for use in asymmetric magnet systems.
One method that is known in the art for generating homogeneous fields over a volume that is asymmetric to the coil structure is to enclose one end of the cylindrical structure, a so-called xe2x80x98end-capxe2x80x99 or dome structure (details of which are given by Meyer and Ballon in The Journal of Magnetic Resonance, 107, 19 (1995) and by Hayes in SMRM 5th annual meeting, Montreal, Book of Abstracts, 39 (1986)). These designs were applied to structures that surrounded only the head of a patient and, by their nature, prevent access to the top of the head. The limited access also makes these structures problematic for whole-body imaging as they substantially reduce access from one end of the magnet.
It is an object of this invention to provide coil structures that generate desired RF fields within certain specific, and asymmetric portions of the overall coil structure, preferably without substantially limiting access from one end of the structure. Asymmetric radio frequency coils can be used in conventional MR systems or in the newly developed asymmetric magnets of U.S. Pat. No. 6,140,900.
It is a particular object of the present invention to provide a general systematic method for producing a desired radio frequency field within a coil, using a full-wave, frequency specific technique to first define a current density on at least one cylindrical surface and subsequently to synthesize a coil pattern from the current density.
It is a further particular object of the present invention to use complex current densities in the full-wave, frequency specific method.
In one broad form, the invention in accordance with certain of its aspects provides a coil structure for a magnetic resonance device having a cylindrical space with open ends, the coil structure being adapted to generate a desired RF field within a specified portion of the cylindrical space. In accordance with the product aspects of the invention, this portion is asymmetrically located relative to the mid-length point of the longitudinal axis of the cylindrical space.
In connection with another aspect, the invention provides a method for manufacturing a radio frequency coil structure for a MR device having a cylindrical space, preferably with open ends, comprising the steps of
selecting a target region over which a transverse RF magnetic field of a predetermined frequency is to be applied by the coil structure, the target region being preferably asymmetrically located relative to the mid-length point of the longitudinal axis of the cylindrical space,
calculating current density at the surface of the cylindrical space required to generate the target field at the predetermined frequency,
synthesizing a design for the coil structure from the calculated current density in accordance with one of the methods discussed below, and
forming a coil structure according to the synthesized design.
Preferably, the method for calculating the current density uses a time harmonic method that accounts for the frequency of operation of the RF coil structure and makes use of a complex current density.
The RF coils of the invention can be used as transmitter coils, receiver coils, or both transmitter and receiver coils. As discussed above, when the coil serves a transmitting function, it will normally be combined with a shield to reduce magnetic interference with external components of the magnetic resonance imaging system. To avoid redundancy, the following summary of the method aspects of the invention is in terms of a RF coil system which includes a main coil (corresponding to the xe2x80x9cfirst complex current densityxe2x80x9d) and a shielding coil (corresponding to the xe2x80x9csecond complex current densityxe2x80x9d), it being understood that these methods can be practiced with just a main coil.
In accordance with a first method aspect of the invention, which can be used under xe2x80x9cmildxe2x80x9d coil length to wavelength conditions, i.e., conditions in which the coil length is less than about one-fifth of the operating wavelength, a method for designing apparatus for transmitting a radio frequency field (e.g., a field having a frequency of at least 20 Megahertz, preferably at least 80 Megahertz), receiving a magnetic resonance signal, or both transmitting a radio frequency field and receiving a magnetic resonance signal is provided which comprises:
(a) defining a target region (e.g., a spherical or ellipsoidal region preferably having a volume of at least 30xc3x97103 cm3 and asymmetrically located relative to the midpoint of the RF coil, e.g., the ratio of the distance between the midpoint of the target region and one end of the coil to the length of the coil is less than or equal to 0.4) in which the radial magnetic component (e.g., Bx, By, or combinations of Bx and By) of the radio frequency field is to have desired values (e.g., substantially uniform magnitudes), said target region surrounding a longitudinal axis, i.e., the common longitudinal axis of the magnetic resonance imaging system and the RF coil;
(b) specifying desired values for said radial magnetic component of the radio frequency field at a preselected set of points within the target region (e.g., a set of points distributed throughout the target region or a set of points distributed at the outer boundary of the target region);
(c) defining a target surface (e.g., the shield coil surface) external to the apparatus on which the magnetic component of the radio frequency field is to have a desired value of zero at a preselected set of points on said target surface;
(d) determining a first complex current density function, having real and imaginary parts, on a first specified cylindrical surface (i.e., the main coil surface) and a second complex current density, having real and imaginary parts, on a second specified cylindrical surface (i.e., the shield coil surface), the radius of the second specified cylindrical surface being greater than the radius of the first specified cylindrical surface (e.g., the radius of the second surface can be 10% greater than the radius of the first surface) by:
(i) defining each of the complex current density functions as a sum of a series of basis functions (e.g., triangular and/or pulse or sinusoidal and/or cosinusoidal functions) multiplied by complex amplitude coefficients having real and imaginary parts; and
(ii) determining values for the complex amplitude coefficients using an iterative minimization technique (e.g., a linear steepest descent or a conjugate gradient descent technique) applied to a first residue vector obtained by taking the difference between calculated field values obtained using the complex amplitude coefficients at the set of preselected points in the target region and the desired values at those points and a second residue vector equal to calculated field values obtained using the complex amplitude coefficients at the preselected set of points on the target surface; and
(e) converting said first and second complex current density functions into sets of capacitive elements (as understood by persons skilled in the art, such capacitive elements will in general have some inductive and resistive properties) and sets of inductive elements (as understood by persons skilled in the art, such inductive elements will in general have some capacitive and resistive properties) located on the specified cylindrical surfaces by:
(i) converting each of the first and second complex current density functions into a curl-free component Jcurl-free and a divergence-free component Jdiv-free using the relationships:
Jcurl-free=∇"psgr", and 
Jdiv-free=∇xc3x97S, 
xe2x80x83where "psgr" and S are functions obtained from the respective first and second complex current density functions through the equations:
∇2"psgr"=∇xc2x7J, 
xe2x88x92∇2S=∇xc3x97J, and 
xe2x88x92∇2(nxc2x7S)=nxc2x7∇xc3x97J, 
xe2x80x83where n is a vector normal to the respective first and second specified cylindrical surfaces and J is the respective first and second complex current density functions;
(ii) calculating locations on the respective first and second cylindrical surfaces for the respective sets of capacitive elements by contouring the respective "psgr" functions; and
(iii) calculating locations on the respective first and second cylindrical surfaces for the respective sets of inductive elements by contouring the respective functions nxc2x7S ("psgr" and nxc2x7S are referred to herein and function as xe2x80x9cstreaming functionsxe2x80x9d).
In accordance with a second method aspect of the invention, which can be used under xe2x80x9cnon-mildxe2x80x9d coil length to wavelength conditions, i.e., conditions in which the coil length can be greater than about one-fifth of the operating wavelength, a method for designing apparatus for transmitting a radio frequency field or both transmitting a radio frequency field and receiving a magnetic resonance signal is provided which comprises:
(a) defining a target region in which the radial magnetic component of the radio frequency field is to have desired values, said target region surrounding a longitudinal axis, i.e., the common longitudinal axis of the magnetic resonance imaging system and the RF coil;
(b) specifying desired values for said radial magnetic component of the radio frequency field at a preselected set of points within the target region;
(c) defining a target surface external to the apparatus on which the magnetic component of the radio frequency field is to have a desired value of zero;
(d) determining a first complex current density function, having real and imaginary parts, on a first specified cylindrical surface and a second complex current density, having real and imaginary parts, on a second specified cylindrical surface, the radius of the second specified cylindrical surface being greater than the radius of the first specified cylindrical surface:
(i) defining each of the complex current density functions as a sum of a series of basis functions (e.g., sinusoidal and/or cosinusoidal functions) multiplied by complex amplitude coefficients having real and imaginary parts; and
(ii) determining values for the complex amplitude coefficients by simultaneously solving matrix equations of the form:                                                         [                              A                1                C                            ]                        ⁢                          (                              a                C                            )                                +                                    [                              A                1                S                            ]                        ⁢                          (                              a                S                            )                                      =                                                                              B                  C                                ⁢                                  
                                [                                  A                  2                  C                                ]                            ⁢                              (                                  a                  C                                )                                      +                                          [                                  A                  2                  S                                ]                            ⁢                              (                                  a                  S                                )                                              =                      B            S                                              (                  Eq          .                      xe2x80x83                    ⁢          I                )            
xe2x80x83where A1C, A1S, A2C, and A2S are transformation matrices between current density space and magnetic field space whose components are based on time harmonic Green""s functions, aC and aS are vectors of the unknown complex amplitude coefficients for the first and second complex current density functions, respectively, BC is a vector of the desired values for the radial magnetic field specified in step (b), and BS is a vector whose values are zero, said equations being solved by:
(1) transforming the equations into functionals that can be solved using a preselected regularization technique, and
(2) solving the functionals using said regularization technique to obtain values for the complex amplitude coefficients; and
(e) converting said first and second complex current density functions into sets of capacitive elements and sets of inductive elements located on the specified cylindrical surfaces (preferably, this step is performed using the methods of step (e) of the first method aspect of the invention; also the methods of said step (e) can be used independent of either the first or second method aspects of the invention to convert a complex current density function to sets of capacitive and inductive elements, i.e., to a manufacturable coil structure).
In accordance with certain preferred embodiments of this second method aspect of the invention, the regularization functional is chosen so as to minimize the integral of the dot product of the first complex current density function with itself over the first specified cylindrical surface and to minimize the integral of the dot product of the second complex current density function with itself over the second specified cylindrical surface. Other regularization functionals that can be used include: (1) the second derivative of the complex current density functions, and (2) other functionals besides the dot product that are proportional to the square of the complex current density functions.
In accordance with other preferred embodiments, the complex amplitude coefficients are chosen so that the first and second complex current density functions each has zero divergence.
The parenthetical statements set forth in connection with the summary of the first method aspect of the invention also apply to the second method aspect of the invention except where indicated. In connection with all of its method aspects, the invention also preferably includes the additional step(s) of displaying the locations of the sets of inductive elements on the first and second specified cylindrical surfaces and/or producing physical embodiments of those sets of elements.
In accordance with certain of its product aspects, the invention provides apparatus for use in a magnetic resonance system for transmitting a radio frequency field (e.g., a field having a frequency greater than, for example, 20 megahertz, and preferably greater than 80 megahertz), receiving a magnetic resonance signal, or transmitting a radio frequency field and receiving a magnetic resonance signal, said apparatus and said magnetic resonance imaging system having a common longitudinal axis, said apparatus comprising:
(a) a support member (e.g., a tube composed of fiberglass, TEFLON, or other materials, which preferably can be used as a substrate for a photolithography procedure for printing conductive patterns and which does not substantially absorb RF energy) which defines a bore (preferably a cylindrical bore) having first and second open ends which are spaced from one another along the longitudinal axis by a distance L (the open ends are preferably both sized to receive a patient""s body part which is to be imaged, e.g., the head, the upper torso, the lower torso, a limb, etc.); and
(b) a plurality of inductive elements (e.g., copper or other metallic tracks or tubes) and a plurality of capacitive elements (e.g., distributed or lumped elements) associated with the support member (e.g., mounted on and/or mounted in and/or mounted to the support member);
wherein if used as a transmitter, the apparatus has the following characteristics (the xe2x80x9cif used as a transmitterxe2x80x9d terminology is used in defining both transmitting and receiving RF coils since by reciprocity, coils that transmit uniform radio frequency fields, receive radio frequency fields with a uniform weighting function):
(i) the apparatus produces a radio frequency field which has a radial magnetic component which has a spatially-varying peak magnitude whose average value is Ar-avg;
(ii) the apparatus has a homogenous volume within the bore over which the spatially-varying peak magnitude of the radio frequency field has a maximum deviation from Ar-avg which is less than or equal to 15% (preferably less than or equal to 10%);
(iii) the homogeneous volume defines a midpoint M which is on the longitudinal axis, is closer to the first end than to the second end, and is spaced from the first end by a distance D such that the ratio D/L is less than or equal to 0.4 (preferably less than or equal to 0.25); and
(iv) at least one of said inductive elements (e.g., 1, 2, 3, . . . or all) comprises a discrete conductor (e.g., a copper or other metallic track or tube) which follows a sinuous path such that during use of the apparatus current flows through a first part of the conductor in a first direction that has both longitudinal and azimuthal components and through a second part of the conductor in a second direction that has both longitudinal and azimuthal components, said first and second directions being different. An example of such a sinuous path is shown in FIG. 15 discussed below.
In certain preferred embodiments, the homogenous volume is at least 30xc3x97103 cm3 and/or L is at least 1.0 meter.
In other preferred embodiments, the first and second open ends have transverse cross-sectional areas A1 and A2, respectively, which satisfy the relationship:
|A1xe2x88x92A2|/A1 less than 0.1.
where A1 is preferably at least 2xc3x97103 cm2.
In connection with all of the aspects of the invention, the lengths of coils and of cylindrical spaces associated therewith are defined in terms of the inductive elements making up the coil. In particular, for a horizontally oriented coil, the length constitutes the distance along the longitudinal axis from the leftmost edge of the leftmost inductive element to the rightmost edge of the rightmost inductive element, corresponding definitions applying to other orientations of the coil.